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Fixed point results on a metric space endowed with a finite number of graphs and applications

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Abstract

In this paper, we consider self-mappings defined on a metric space endowed with a finite number of graphs. Under certain conditions imposed on the graphs, we establish a new fixed point theorem for such mappings. The obtained result extends, generalizes and improves many existing contributions in the literature including standard fixed point theorems, fixed point theorems on a metric space endowed with a partial order and fixed point theorems for cyclic mappings.

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References

  1. R. P. Agarwal, M. A. El-Gebeily, D. O’Regan: Generalized contractions in partially ordered metric spaces. Appl. Anal. 87 (2008), 109–116.

    Article  MATH  MathSciNet  Google Scholar 

  2. S. M. A. Aleomraninejad, S. Rezapour, N. Shahzad: Some fixed point results on a metric space with a graph. Topology Appl. 159 (2012), 659–663.

    Article  MATH  MathSciNet  Google Scholar 

  3. I. Altun, H. Simsek: Some fixed point theorems on ordered metric spaces and application. Fixed Point Theory Appl. (2010), Article ID 621469, 17 pages.

  4. I. Beg, A. R. Butt, S. Radojević: The contraction principle for set valued mappings on a metric space with a graph. Comput. Math. Appl. 60 (2010), 1214–1219.

    Article  MATH  MathSciNet  Google Scholar 

  5. T. G. Bhaskar, V. Lakshmikantham: Fixed point theorems in partially ordered metric spaces and applications. Nonlinear Anal. 65 (2006), 1379–1393.

    Article  MATH  MathSciNet  Google Scholar 

  6. D. W. Boyd, J. S. W. Wong: On nonlinear contractions. Proc. Am. Math. Soc. 20 (1969), 458–464.

    Article  MATH  MathSciNet  Google Scholar 

  7. S. K. Chatterjea: Fixed-point theorems. C. R. Acad. Bulg. Sci. 25 (1972), 727–730.

    MATH  MathSciNet  Google Scholar 

  8. Lj. B. Ćirić: Generalized contractions and fixed-point theorems. Publ. Inst. Math., Nouv. Sér. 12 (1971), 19–26.

    Google Scholar 

  9. Lj. B. Ćirić, N. Cakić, M. Rajović, J. S. Ume: Monotone generalized nonlinear contractions in partially ordered metric spaces. Fixed Point Theory Appl. (2008), Article ID 131294, 11 pages.

  10. R. Espínola, W. A. Kirk: Fixed point theorems in ℝ-trees with applications to graph theory. Topology Appl. 153 (2006), 1046–1055.

    Article  MATH  MathSciNet  Google Scholar 

  11. G. E. Hardy, T. D. Rogers: A generalization of a fixed point theorem of Reich. Can. Math. Bull. 16 (1973), 201–206.

    Article  MATH  MathSciNet  Google Scholar 

  12. J. Harjani, K. Sadarangani: Fixed point theorems for weakly contractive mappings in partially ordered sets. Nonlinear Anal. 71 (2009), 3403–3410.

    MATH  MathSciNet  Google Scholar 

  13. J. Jachymski: The contraction principle for mappings on a metric space with a graph. Proc. Am. Math. Soc. 136 (2008), 1359–1373.

    MATH  MathSciNet  Google Scholar 

  14. R. Kannan: On certain sets and fixed point theorems. Rev. Roum. Math. Pures Appl. 14 (1969), 51–54.

    MATH  Google Scholar 

  15. W. A. Kirk, P. S. Srinivasan, P. Veeramani: Fixed points for mappings satisfying cyclical contractive conditions. Fixed Point Theory 4 (2003), 79–89.

    MATH  MathSciNet  Google Scholar 

  16. J. J. Nieto, R. Rodríguez-López: Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations. Order 22 (2005), 223–239.

    MATH  MathSciNet  Google Scholar 

  17. J. J. Nieto, R. Rodríguez-López: Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations. Acta Math. Sin., Engl. Ser. 23 (2007), 2205–2212.

    MATH  MathSciNet  Google Scholar 

  18. A. Petruşel, I. A. Rus: Fixed point theorems in ordered L-spaces. Proc. Am. Math. Soc. 134 (2006), 411–418.

    MATH  Google Scholar 

  19. A. C. M. Ran, M. C. B. Reurings: A fixed point theorem in partially ordered sets and some applications to matrix equations. Proc. Am. Math. Soc. 132 (2004), 1435–1443.

    MATH  MathSciNet  Google Scholar 

  20. B. Samet: Coupled fixed point theorems for a generalized Meir-Keeler contraction in partially ordered metric spaces. Nonlinear Anal. 72 (2010), 4508–4517.

    MATH  MathSciNet  Google Scholar 

  21. B. Samet, C. Vetro: Coupled fixed point theorems for multi-valued nonlinear contraction mappings in partially ordered metric spaces. Nonlinear Anal. 74 (2011), 4260–4268.

    MATH  MathSciNet  Google Scholar 

  22. T. Suzuki: A generalized Banach contraction principle that characterizes metric completeness. Proc. Am. Math. Soc. 136 (2008), 1861–1869.

    MATH  Google Scholar 

  23. M. Turinici: Abstract comparison principles and multivariable Gronwall-Bellman inequalities. J. Math. Anal. Appl. 117 (1986), 100–127.

    MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. FST Campus Universitaire, 2092-El, Manar Tunis, Tunis, Tunisia

    Hajer Argoubi

  2. Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh, 11451, Saudi Arabia

    Bessem Samet

  3. A. Myller Mathematical Seminar, A. I. Cuza University, 700506, Iaşi, Romania

    Mihai Turinici

Authors
  1. Hajer Argoubi
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  2. Bessem Samet
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  3. Mihai Turinici
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Corresponding author

Correspondence to Hajer Argoubi.

Additional information

The authors extend their appreciation to the Deanship of Scientific Research at King Saud University for funding the work through the research group Project (RGP-VPP 237).

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Argoubi, H., Samet, B. & Turinici, M. Fixed point results on a metric space endowed with a finite number of graphs and applications. Czech Math J 64, 241–250 (2014). https://doi.org/10.1007/s10587-014-0097-6

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  • DOI: https://doi.org/10.1007/s10587-014-0097-6

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